The combo you've described doesn't quite work (for a few reasons), but a lesser cousin could.

Tunnel Fighter: ...As a bonus action, you can enter a defensive stance that lasts until the start of your next turn. While in your defensive stance, you can make opportunity attacks without using your reaction, and you can use your reaction to make a melee attack against a creature that moves more than 5 feet while within your reach.

So, Tunnel Fighter lets you (if properly prepared) make opportunity attacks without spending your reaction. Cool. It also, independently, gives you a way to make a reaction attack (not an opportunity attack) if someone moves around in your reach, under that same preparation. Okay.

Polearm Master: ...While you are wielding a glaive, halberd, pike, or quarterstaff, other creatures provoke an opportunity attack from you when they enter your reach.

Polearm Master lets you take an opportunity attack when someone comes into your reach. Cool.

War Caster: ...When a hostile creature's movement provokes an opportunity attack from you, you can use your reaction to cast a spell at the creature, rather than making an opportunity attack. The spell must have a casting time of 1 action and must target only that creature.

War Caster lets you use your reaction to cast an attack spell when someone provokes an opportunity attack from you (which, among other things, would let you case eldritch blast with repelling blast, if you were able to cast it otherwise.)

So, this is where your description breaks down. Suppose you have a polearm with reach 2, and are in your stance. The enemy enters reach 2. This triggers your Polearm Mastery opportunity attack, which you could convert into an Eldritch Blast. If you do not convert it, it's still an opportunity attack, and therefore does not cost you a reaction. You choose not to convert, and take your free opportunity attack. At that point, the enemy steps forward one more, triggering your tunnel fighter reaction attack... but that's not an opportunity attack, and therefore cannot be converted. You can hit him again, but it won't knock him back.

Now, that's not to say you get nothing from this. In particular, you can still take advantage of your polearm mastery attack twice. The first time he steps within 2, you use eldritch blast on your polearm mastery opportunity attack (consuming your reaction). This knocks him back, and forces him to approach again, at which point you can hit him again. Unfortunately, having done that you don't get to hit him yet another time with your Tunnel Fighter reaction attack because you already used your reaction on War Caster.

Even with that more limited version, though, There's still one caveat to get through. The build you described still doesn't quite work because Warlock doesn't get invocations until 2nd level, and thus can't have repelling blast before that point. That's a lesser issue, though. All you need to do is grab a second level in Warlock (and probably Agonizing Blast as well). You might want to take it as high as 3rd level warlock (or 4th, for the stat bump) in order to get the Hexblade/Pact of the Blade combo that lets you use charisma as your weapon attack stat. That's losing you a fair number of fighter levels, though.

Not quite

There is no trigger for the second opportunity attack (Eldritch Blast), because the enemy is not leaving the PC's zone of control (which would trigger a normal AoO), nor is the attack granted via Tunnel Fighter for an enemy moving within 5 feet of the PC an opportunity attack (it's specifically a melee attack in exchange for a reaction). War Caster is explicitly triggered only by an opportunity attack, so no chance for an attack of opportunity, no EB.

If the PC had used the previous turn's Action to ready EB on the trigger that an enemy moves within 5 feet of them, you could get the same effect, but that's a pretty different and less flexible scenario.

This does not work.

Your second opportunity attack is not an opportunity attack, rather, you are using your reaction per this clause from Tunnel Fighter:

you can use your reaction to make a melee attack against a creature that moves more than 5 feet while within your reach.

Notice "opportunity attack" is absent from this portion of the fighting style description, so it is not an opportunity attack.

War caster says:

When a hostile creature's movement provokes an opportunity attack from you, you can use your reaction to cast a spell at the creature, rather than making an opportunity attack.

Since the creature did not provoke an opportunity attack, you cannot use war caster to cast eldritch blast.